Optical sky-sun diffuser

ABSTRACT

An embodiment of a solid optical sky-sun diffuser, which comprises a transparent solid matrix embedding a dispersion of transparent nanoparticles having an average size d in the range 10 nm≤d≤240 nm; wherein: the ratio between the blue and red scattering optical densities γ≡Log [T(450 nm)]/Log [T(630 nm)] of said diffuser falls in the range 5≥γ≥2.5, where T(λ) is the Monochromatic Normalized Collinear Transmittance; in at least one propagation direction, said Monochromatic Normalized Collinear Transmittance is T(450 nm)≥0.4; in at least one propagation direction said Monochromatic Normalized Collinear Transmittance is T(450 nm)≤0.9, said propagation direction being the same or different from that at which said Monochromatic Normalized Collinear Transmittance is T(450 mm)≥0.4.

More than one reissue application has been filed for the reissue of U.S.Pat. No. 8,469,550. The reissue applications are: U.S. application Ser.No. 15/491,632 (the present application) and U.S. application Ser. No.14/747,158, now U.S. Pat. No. RE 46,418. U.S. application Ser. No.15/491,632 is a continuation reissue of U.S. application Ser. No.14/747,158.

PRIORITY CLAIM

The present application is a Continuation of International PatentApplication Serial No. PCT/EP2009/057674, filed Jun. 19, 2009; whichfurther claims the benefit of Italian Patent Application MI2008A001135,filed Jun. 24, 2008; all of the foregoing applications are incorporatedherein by reference in their entireties.

RELATED APPLICATION DATA

This application is related to U.S. patent application Ser. No.13/001,050, entitled ILLUMINATION DEVICE filed Apr. 27, 2011, and whichis incorporated herein by reference in its entirety.

TECHNICAL FIELD

An embodiment relates to an optical sky-sun nanodiffuser. In the presentdescription the term “sky-sun nanodiffuser” designates an opticaldiffuser that simulates the diffusion of the sun light operated by thesky in nature. Particularly, an embodiment relates to an opticalnanodiffuser of the type comprising a transparent solid matrix in whicha plurality of solid transparent nanoparticles are dispersed. In thepresent description the term “nanodiffuser” designates a solid opticalelement which comprises a transparent solid matrix embedding adispersion of transparent nanoparticles, whose average size d is in therange 10 nm≤d≤240 nm. In the following of the description the term“nanodiffuser” or “diffuser” may be used interchangeably. In any casethey designate a nanodiffuser as defined above.

BACKGROUND

Optical diffusers comprising solid nanoparticles dispersed in atransparent solid matrix are known in the art.

U.S. Pat. No. 6,791,259 B1, which is incorporated by reference describesa white light illumination system comprising an LED or laser diode, alight scatterer material and a phosphor or luminescent dye material. Thescatterer material preferably comprises particles dispersed in asubstrate. The particles that scatter light have a size between 50 and500 nm, preferably a size between λ/3 and λ/2, where λ is the wavelengthof the emission peak of the radiation source. The nanoscatterer isintegrated at the level of the active element of the source, that is, itis positioned either before the phosphor or in the phosphor, in order toscatter preferably the blue component produced by the LED or laserdiode, otherwise with low divergence, and to uniform it with the yellowcomponent scattered by the phosphor, instead produced with a wide angleof divergence. The fact that the two yellow and blue components arescattered from practically coincident scatterer centers is a necessarycondition to remove the “halo” phenomenon, characterized by the presenceof a dominant blue color in the direction of maximum emission, and of adominant yellow color in the peripheral area of the light cone producedby the source, that is, to uniform color distribution of the radiationat different angles.

WO 02/089175, which is incorporated by reference, describes lightsources based on UV-LED emitters with reduced dispersion of UVradiation. The light sources are LEDs which emit in the UV and which arecombined with UV reflectors constituted by particles dispersed in asolid material transparent to visible light. A phosphorescent materialis applied to the UV source to convert UV radiation into visible light.In a particular embodiment the phosphorescent material is applied to thesurface of the UV LED and a layer of scatterer material is applied tothe phosphorescent layer. The aim of this illumination device structureis to reduce the amount of UV radiation not converted into visible lightand does not tackle the problem of reproducing a light similar tonatural light produced by the sun and the sky.

US 2008/0262117 A1, which is incorporated by reference, describes adiffused light transmitter comprising a substantially transparent resinin which nanometric size amorphous silica particles are dispersed. Inone example a material having a Haze of 71-85% and a Light Transmittanceof 35-40% is reported.

None of the documents above discloses an optical sky-sun diffuser,namely a diffuser capable to carry out chromatic separationsubstantially with the same mechanism that gives rise to chromaticseparation in nature, thereby creating the correct spectral distributioncharacteristic of skylight and sunlight.

SUMMARY

Accordingly, an embodiment is a new type of optical diffuser capable of“separating” different chromatic components of a source with broadspectral bandwidth according to the same mechanism that gives rise tochromatic separation in nature, creating the correct spectraldistribution characteristic of skylight and sunlight.

More particularly, an embodiment is a new type of optical diffusercapable of reproducing—when illuminated by visible white light—thesimultaneous presence of two different chromatic components: a diffusedskylight, in which blue (“cold”) is dominant, and a transmittedsunlight, with a low blue component (“warm”).

The aforesaid and other objects and advantages may be achieved with anembodiment of a solid optical sky-sun diffuser which comprises atransparent solid matrix embedding a dispersion of transparentnanoparticles, characterized in that:

-   -   said nanoparticles have an average size d in the range 10        nm≤d≤240 nm,    -   the ratio between the blue and red scattering optical densities)        γ≡Log [T(450 nm)]/Log [T(630 nm)] of said diffuser falls in the        range 5≥γ≥2.5, where T(λ) is the Monochromatic Normalized        Collinear Transmittance,    -   in at least one propagation direction, said Monochromatic        Normalized Collinear Transmittance is T(450 nm)≥0.4,    -   in at least one propagation direction, said Monochromatic        Normalized Collinear Transmittance is T(450 nm)≤0.9, said        propagation direction being the same or different from that at        which said Monochromatic Normalized Collinear Transmittance is        T(450 nm)≥0.4.

The average particle size is defined in the following of the presentdescription and the Monochromatic Normalized Collinear Transmittance, inthe following simply called “Transmittance”, is defined by means of themeasurement method illustrated in the present description.

BRIEF DESCRIPTION OF THE DRAWINGS

The macroscopic optical properties of the sky-sun diffuser of one ormore embodiments are discussed in the following.

The enclosed figures and drawings illustrate one or more embodiments.

FIG. 1 shows a particular arrangement of the panel nanodiffuser where alight source, or an array of light sources, as for example an LED array,has been coupled to the diffuser from one side, to operate it as asunset skylike diffuser, said sunset skylike diffuser being described atpage 8 of the present description.

FIG. 2 shows the construction of a sun-color filter, composed by aplurality of individual nano-diffusers according to an embodiment,joined in a multi-channel structure where each diffuser is separatedfrom the others by an absorbing interface which absorbs all thescattered light. Details of the absorbing interface are shown at thebottom of the figure.

FIG. 3A illustrates a particular layout where a plurality of sun filtersworking on the basis of the principle illustrated in FIG. 2 is used inorder to vary the tinge of the artificial sun light. FIG. 3B shows thelayout where a plurality of noon skylike diffusers according to anembodiment and of absorbing multi-channel structures are combined toobtain a sun filter with variable optical density and controlledmultiple scattering, said noon skylike diffusers being described at page7 of the present description

FIG. 4 shows the contour plot of the function γ(m,D), where m is therelative refraction index and D the effective diameter defined in thepresent description;

FIG. 5 shows the calculated, angularly resolved, scattering color maps,for four m,D pairs and corresponding γ(m,D) values;

FIG. 6 shows the volume in the (m,D,N) space corresponding to the case5≥γ(m,D)≥3 and 0≤N≤N_(max) where N is the total number of particles perunit area seen by a light beam propagating in a given direction andN_(max) is defined in the present description;

FIG. 7 shows the volume in the (m,D,N) space corresponding to the case5≥γ(m,D)≥3 and N_(min)≤N≤10²⁸ m⁻² where N_(min) is defined in thepresent description;

FIG. 8 schematically illustrates few examples of the possiblemacroscopic morphology of the nano-diffuser according to an embodiment;

FIG. 9 schematically illustrates the experimental apparatus to be usedto measure the “Monochromatic Normalized Collinear Transmittance”;

FIG. 10 schematically illustrates the experimental apparatus to be usedto measure the “Monochromatic Normalized Collinear Transmittance” in theparticular case where the diffuser presents a reflecting surface;

FIG. 11 (top) illustrates the effect of Rayleigh back scattering whenthree sky-sun nanodiffuser disks are front illuminated by a commercialInGaN white LED, and seen against a dark background, while FIG. 11(bottom) shows the effect of the light which is scattered by the samedisks when the light comes from a side.

DETAILED DESCRIPTION

It is well known from fundaments of light-scattering that a transparentoptical element comprising transparent matrix and transparentnano-particles having different refraction index with respect to thematrix, and having average size significantly smaller than visiblewavelength, will preferentially scatter the blue part of the spectrum,and transmit the red part. It is also known that the outlined chromaticseparation improves for smaller sizes, the wavelength-dependence of thescattering efficiency per single particle approaching with good accuracythe λ⁻⁴ Rayleigh limit law when the average particle size is d≤λ/10. Onincreasing the particle size, in contrast, resonances and diffractioneffects start to play a role, and become relevant typically for d≥λ/2.These phenomena may cause a flattening of the wavelength-dependence inthe scattered light. Moreover, they may cause an impinging white sourceto be separated in a plurality of different colors at different angles,which is of course a strongly undesired effect for the purpose of anembodiment. On the other hand, it is known that the scatteringefficiency per single particle drops dramatically on decreasing particlesize, being proportional to d⁻⁶. This dependence makes the usage of toosmall particle inconvenient, as for example for the thickness of thediffuser which is used. In fact, achieving the necessary scatteringefficiency by means of a diffuser based on small particles may requirethe light beam to see a high number of particles in the propagationdirection. This condition may require medium-large thicknesses of thediffuser to be used, in order to prevent high volume-filling-fractioneffects to take place, these filling-fraction effects being thosedescribed in the present description. For example, the request of notexceeding filling fractions of 0.1% sets to about 1 mm the minimumthickness of the diffuser for 50 nm TiO₂ nanoparticles in PMMA, thefigure increasing substantially if smaller particles are used.

Therefore, for those applications for which the use of mm-cm thickdiffusers does not represent a problem, small size particles, forexample in the Rayleigh range d≤λ/10 are recommended. In contrast, forthose applications which benefit from the use of more compact diffusersa compromise between compactness and scattering quality may beconsidered, for which particle size d>λ/10 may be preferentially used.Moreover, the usage of small particles is also convenient for thepurpose of minimizing the risk that aggregates composed of few particlesspoil the quality of the scattering process. The scattering, in fact, isvery sensitive even to a small fraction of these aggregates, due to thed⁻⁶ dependence of scattering efficiency on particle size. Being the sizeof the aggregates proportional to that of the constituent particles, itis evident that in the case of larger particles there is an increase ofthe risk of producing resonances and diffraction effects, which mayrepresent a problem for an embodiment. Therefore the usage of largeparticles may require a special care in the nano-diffuser materialpreparation, in order to ensure that aggregates do no play a relevantrole.

For the purpose of an embodiment, the following condition is satisfied:10 nm≤d≤240 nm, for example 20 nm≤d≤100 nm, such as 20 nm≤d≤50 nm, forthose applications for which thick diffusers may be used. 10 nm≤d≤240nm, for example 50 nm≤d≤180 nm, such as 70 nm≤d≤120 nm, for thoseapplications for which compact devices are preferred. In both cases, drefers to the average size of the particles embedded in the diffuser.This condition does not forbid that in the diffuser are present also fewparticles with dimensions outside this range, but these particles shouldbe in such a small quantity as to have negligible effects on the opticalproperties of the diffuser.

The choice of a correct average size range may be a necessary but by farnot sufficient condition for ensuring the nanodiffuser to performaccording to the scope of an embodiment, i.e. as the sky does with thelight of the sun. First of all, depending on the chosen materials,conditions exist for which the undesired optical resonance anddiffraction effects occur also for particle sizes d≤240 nm. Moreover,plenty of other effects, as for example those related to number ofparticles, to their concentration, to the geometrical shape of thediffuser, might dominate, which may prevent the desired chromaticseparation to take place. To this end it is worth mentioning that otherapplications exist, or have been proposed, that comprise transparentnano-composites having particle sizes in ranges partially overlappedwith the range here considered for which, however, chromatic separationand in some cases even visible scattering are not desired at all. Forexample, applications in LCD diffusers often use nanoparticles with sizeas large as 100 nm, as for example for the purpose of changing theaverage refraction index of a material, in the absence of anychromatic-separation effects [US2004/0233526, which is incorporated byreference]. On the other hand, thin-film UV filter applications, forwhich the absence of Haze in the visible is a fundamental request, areclaimed with particles as large as 20 nm. [WO2007/043496 A1, which isincorporated by reference]

Surprisingly, in spite of the overall problem complexity, it has beenfound that a set of three, easily testable, conditions may guarantee a10 nm≤d≤240 nm nanodiffuser to be adequate for the purposes of anembodiment. All these conditions concern macroscopic optical propertiesof the nanodiffuser at two specific wavelengths, which may be verifiedby measuring the nanodiffuser Transmittance, T(λ), at these wavelengths.

A first optical property of a nanodiffuser of an embodiment isdesignated here as “sun-like” Transmittance. This is one of the opticalproperties that the nanodiffuser has in order to correctly simulate thediffusion of the sun light operated by the sky in nature, andspecifically it refers to the capability of the diffuser to create atransmitted light having the colors characteristic of the light of thesun in the different hours of the day. In other terms, the diffuser ofan embodiment modifies the spectrum of a white-light source that istransmitted through it in a given direction as the sky does with thelight of the sun.

The light-scattering in the sky is well described by Rayleigh diffusion,T_(sky)(λ)≈exp(−bLλ⁻⁴), where b is a constant which depends on theaverage scattering efficiency of the atmosphere, and L is the pathlength. This dependence explains why, on increasing the path length inthe different hours of the day, the transmitted sun light becomes yellowand then red. For any pair of wavelengths of visible light, the skytherefore satisfies with good accuracy the Rayleigh limit, which statesthat the ratio between the sky optical densities at two wavelengthsscales with the fourth power of the inverse of the ratio of thewavelengths, Log [T_(sky)(λ₁)]/Log [T_(sky)(λ₂)]≈(λ₁/λ₂)⁻⁴, where therelation does not depend on path length. Specifically, taking as areference wavelengths λ₁=450 nm and λ₂=630 nm, and by defining the ratiobetween the optical densities at 450 nm and 630 nm, γ≡Log [T(450nm)]/Log [T(630 nm)] the measured air scattering in standard conditionsat 15° C. [A. Bucholtz “Rayleigh-scattering calculations for theterrestrial atmosphere” Applied Optics, Vol 34 p. 2765 (1995), which isincorporated by reference] gives γ_(sky)=3.9606, while (λ₁/λ₂)⁻⁴=3.8416.

In principle, conditioning the nanodiffuser Transmittance T(λ) tofulfill Rayleigh scattering for the entire visible spectrum allowsachieving the desired “sun-like” Transmittance. Surprisingly, it hasbeen found that a nanodiffuser fulfilling the following much more simplecondition:“5≥γ2.5, for example 5≥γ3, such as 5≥γ≥3.5”,which depends only on the nanodiffuser T(450 nm) and T(630 nm), sufficesto potentially guarantee that when the nanodiffuser is illuminated by abroad-band white source, the transmitted light is perceived with thesame color as that of the sun light which has crossed the sky, with thewhole variety of tinges made achievable when diffusers having differentoptical thicknesses are used, according to the scope of an embodiment.

A second optical property of a nanodiffuser of an embodiment isdesignated here as “noon skylike diffusion”. This is a further opticalproperty that the nanodiffuser has in order to correctly simulate thediffusion of the sun light operated by the sky in nature, andspecifically it refers to the capability of the diffuser to scatter theimpinging white light by producing a diffused light having the samecolor as the light diffused by the sky, when the sun is close to theZenith, i.e. at noon or during late morning or early-afternoon time. Tothis purpose it is worth noting that the condition γ≥2.5 determines thequality of the transmitted light but not of the scattered light. Infact, it imposes no limitations on the amount of multiple scattering,which might severely impact the spectral features of the scatteredlight. Indeed, for strong multiple scattering all the impinging lightspectral components are usually evenly diffused, which makes thediffused light to take the same color as that of the source (typicallywhite). Since the probability of multiple scattering, for a givenwavelength and propagation direction, depends only on T(λ), beingmaximum when Transmittance is zero, minimizing multiple scatteringimplies working in high Transmittance regime, which may cause a drawbackon the efficiency.

Surprisingly, it has been found that conditioning the transmission in agiven direction by the constraint:“T(450 nm)≥T_(min), T_(min)=0.4, for example T_(min)=0.5, such asT_(min)=0.6”limits multiple scattering within acceptable limits, in the sense thatthe diffuse light maintains the natural sky-like characteristic tinge,while presenting a scattering power as large as 60% in the blue.Notably, since a beam propagating in a different direction with respectto the diffuser orientation might experience a longer path inside thediffuser, which implies a lower Transmittance, the condition T(450nm)≥T_(min) is considered as valid only for the specified propagationdirection. A propagation direction which fulfills the condition T(450nm)≥T_(min) is called in the following: “high-Transmittance direction”.The diffuser is operated as a noon skylike diffuser when the impinginglight beam propagates in the diffuser in the high Transmittancedirection.

The third optical property of a nanodiffuser of an embodiment isdesignated here as “sunset skylike diffusion”. This is a further opticalproperty that the nanodiffuser satisfies in order to correctly simulatethe diffusion of the sun light operated by the sky in nature, andspecifically it refers to the capability of the diffuser to scatter theimpinging white light by producing the colors of the sky at sunset (orsunrise), i.e. when the sun is close to the horizon. In this condition,the distinguishing feature of the process is that the colors change fromthe blue to the red depending from which particular position in the skythe light is diffused. This request rises immediately a problem, sinceeven the lowest Transmittance admitted for the purpose of avoidingrelevant multiple scattering, T(450 nm)≥0.4, is too high to ensure thatall colors except for orange-red are scattered away, as it is done toadequately reproduce the sky at sunset. In other words, obtainingorange-red from light scattering implies to operate in multiplescattering regime. The question is then how to prevent multiplescattering from spoiling the spectacular sunrise/sunset colordistribution. In nature the problem is solved by the curvature of thesky, which implies that the different portions of the sky seen by theobserver are illuminated by sun rays which have traveled different pathlengths of sky. In other words, at sunset the observer sees red at thehorizon, since the atmosphere scatters the residual light from the lowsun which has crossed a long path in the low sky, while the observersees blue at the Zenith, since the high atmosphere scatters toward usthe sun beams which have crossed only a short path in the sky. A firstoption, therefore, is that of imitating nature by producing a diffuserhaving suitable curvature. This option, however, presents severaltechnical difficulties. Among the other, one should not forget thatwhile in nature sunbeams easily enter the sky at low incidence angle,here the problem of extremely high reflections may appear due to thefact that the diffuser embedding matrix has a refraction index differentfrom that of air. This problem may be solved by embedding the curveddiffusing element into a parallelepiped transparent matrix, made of thesame matrix material in which nanoparticles are dispersed. In this case,since the average refraction index of the matrix and of the nanodiffuserare virtually identical, the reflection of light at the curved diffuserinterface is removed. This setting allows reconstruction of the sky insunset mode, according to an embodiment.

A further scheme is disclosed here, in two different geometries, whichsurprisingly allows to operate a diffuser homogeneously filled withnanoparticles in strong multiple scattering regime, while preserving thepurity of the color distribution of the sky at sunrise/sunset. This isachieved by a diffuser which has low Transmittance in the propagationdirection, and particularly T(λ)<<1 for λ≤570 nm, i.e. for allwavelength components except for orange and red, but large Transmittancein one or both the orthogonal directions, and more precisely T_(⊥)(450nm)≥0.4, for example T_(⊥)(450 nm)≥0.5, such as T_(⊥)(450 nm)≥0.6.

In a first embodiment, a nanodiffuser is shaped as a long and narrowcylinder, with a length L much larger than the diameter, Φ, and which isilluminated along its axis. More precisely, the cylinder has L>10Φ, forexample L>20Φ, such as L>30Φ. In this case the diffuser may be made tohave high Transmittance in both the orthogonal directions, and lowTransmittance in the propagation direction. Setting T(λ)≤0.5, forexample T(λ)≤0.3, such as T(λ)≤0.1 for λ≤570 nm in the propagationdirection, strong multiple scattering will take place, and onlyorange-red photons will reach the end of the diffuser. An observer thatlooks at the diffuser by the side, however, will see dominant blue lightemitted close to the entrance of the cylinder, followed by a greenish,yellowish and finally an orange and red tinge along the entire length ofthe diffuser, different dominant colors being scattered from differentportions of the diffuser, according to the scope of an embodiment.Notably, if all diffused light was mixed, it would be indeed almostwhite. However, since different colors are scattered by differentportions of the diffuser, they will be perceived separately by theobserver. It is noted that the condition for the diffuser to beoptically thin in the orthogonal direction, so that every time onephoton is scattered it leaves the diffuser and it cannot be scatteredagain, is relevant to achieve the desired chromatic separation. In fact,if the diffuser is thick also in the orthogonal directions, showing forexample T_(⊥)(450 nm)<0.4, a blue photon scattered, for example, closeto the entrance of the diffuser may be redirected along the cylinderaxis by a second scattering event, and finally be scattered out at thevery end of the cylinder, eventually overlapping with a red photon whichis scattered for the first time, thus creating a white diffused light,which is not desired for a nanodiffuser according to an embodiment.

In a second embodiment the diffuser is shaped as a flat panel, whoselength (L), height (H) width (W) fulfill L≥H>>W. Notably, here the panelis illuminated from one side, so that the light beam propagates alongthe L direction. It is noted that the propagating beam may be guidedinside the panel due to total internal reflection, as it is alsopossible for the cylinder, with the exception of the component which isscattered out of the diffuser due to the presence of nanoparticles. Inthis panel embodiment, as opposed to the previous case of the cylinder,the diffuser is optically thin only in one of the two orthogonaldirections. As a consequence, a photon which is scattered in the planeof the diffuser may be scattered again in the same plane several times.However, since this scattered photon has a polarization orthogonal tothe panel (i.e. along W), the probability that it is scattered out ofthe diffuser is very low. As a consequence, the probability that photonsof different colors leave the same portion of the diffuser is again low,which may guarantee the necessary conditions for the panel to reproducea spectacular reconstruction of the chromatic distribution of the sky atsunrise/sunset, according to an embodiment.

There are a few configurations of this second embodiment here addressedwhich are remarkable for applications.

(i) For what concerns the dimensions of the panel, it may be convenientto operate with L>10 W, for example L>20 W, such as L>30 W.

(ii) For what concerns surface quality, the two panel large faces arevirtually free from scratches, digs, bubbles or any other defect, sincethese defects will become visible when the light is guided inside thepanel. In general, the quality of the panel surfaces typically guaranteethat the scattering produced by the surface on the internally guidedlight is less than 15%, for example than 5%, such as than 1% than thescattering produced by the nanoparticles. The test may be performed bycomparing the luminosity of the diffuser with and without nanoparticles.

(iii) A particular arrangement of the panel nanodiffuser comprisesinserting into the diffuser or coupling to the diffuser from one side alight source, or an array of light sources, as for example an LED array,as depicted in FIG. 1. The light from the LED is partially guided insidethe panel via total internal reflection and partially scattered out ofthe diffuser panel by means of the action of the nanoparticles.Inserting a light source into the diffuser or coupling it to thediffuser is not to be considered as an option limited to the specificpanel diffuser described in the present example, but it refers to allthe diffusers considered by an embodiment, such as, for example, thecylinder diffuser described in the previous embodiment.

(iv) In a further configuration, the panel is applied on a mirrorsurface, or has a high-reflectivity coating deposited on one of the twolargest faces. This option may be convenient if the panel has to be usedas a furnishing element. In this case, as specified in the measurementmethod described in the present description, the Transmittance acrossthe diffuser may still be measured, in reflection, obtaining as a resultthe value relative to twice the thickness of the panel. However, in thepresence of a mirror applied on the panel, the optical thickness whichneeds to be considered with respect to the limitations imposed bymultiple scattering is indeed twice the thickness of the panel. In otherwords, the panel will behave in respect to the multiple scattering as ifits thickness was twice. Therefore the measurement of double passTransmittance is correct in this regime. It is noted that this reasoningconcerning the implementation of a mirror surface on the nano-diffuserdoes not apply only to this specific configuration, but to allnano-diffusers according to an embodiment.

With respect to the problem of multiple scattering which is addressed inthis paragraph, it has surprisingly been found that a single conditionmay suffice for guaranteeing a generic nanodiffuser optical element tobe adequate for reproducing the light scattered by the sky both fornoon-type and sunset-type regimes. This condition is that there existsat least one propagation direction inside the nanodiffuser for which:T(450 nm)≥T_(min), T_(min)=0.4, for example T_(min)=0.5, such asT_(min)=0.6If the diffuser is illuminated along this high-Transmittance directionit means that it is operated as a noon skylike diffuser. In contrast, ifit is illuminated along an orthogonal direction, over which theTransmittance is lower, then it means that the diffuser is operated assunset skylike diffuser.

The fourth optical property which characterizes a sky-sun diffuser of anembodiment is that of being able to scatter the impinging light beamwith a scattering efficiency comparable to that of the sky, so that whenan object or a scene is illuminated by both the transmitted (sun-like)and diffused (sky-like) light components, the balance between the twocomponents corresponds to what occurs in nature. It has been evaluatedthat in a typical spring day, in the early afternoon, with clear skiesand at a subalpine latitude in Italy, the sky contributes for at least20% of the outdoor luminosity, the rest being due to the transmittedlight of the sun, the figure increasing to 40-50% in late afternoon. Byassuming the back scattering to be suitably minimized, the condition tobe fulfilled by a nanodiffuser according to an embodiment is that thereexists at least one propagation direction inside the nanodiffuser forwhich:“T(450 nm)≤T_(Max), where T_(Max)=0.9, for example T_(Max)=0.8, such asT_(Max)=0.7”

The reason why it may be required that the condition be fulfilled for atleast one, and not for all the directions inside the diffuser, relatesagain with the case of a large aspect ratio diffuser, i.e. those shapedas a thin cylinder or as a panel as described for an embodiment. In thiscase, owing to a very large unbalance between propagation lengths in theorthogonal dimensions, the optimum operating regime may require a fairlyhigh Transmittance in the orthogonal direction. In order to demonstratethe relevance of an embodiment, in what follows are disclosed threepossible applications based on a diffuser according to an embodiment, oron a set of diffusers according to an embodiment, and of different typesof obscurants.

The first application is based on the combination of a sunset-mode panelaccording to an embodiment and an obscurant which covers completely oneof the two large faces of the panel. The presence of the obscurant isbeneficial in order to let an observer to see the light scattered by thediffuser against a dark background, and also in order to maximize colorfidelity. In fact, in nature the sky is always seen against a darkbackground, which is the empty space among the stars. The use of anobscurant surface may be beneficial also when a diffuser is meant to beused in skylike noon mode. In this case, the observer does not have thepossibility to observe the light of the source transmitted by thediffuser. However, the observer may position himself/herself on the sameside as the light source, and observe the diffuser in back-scatteringmode. In this case the presence of the obscurant is mandatory toappreciate the effect, unless the diffuser panel is seen by the observeragainst a naturally dark background. This is the case, for example, whenthe diffuser is used as a domestic window over a dark night scene. Inthis case an observer inside an illuminated apartment will perceive thebackscattered light from the panel, which will appear as the light fromthe sky. It should be remarked that if the obscurant is applied onto thediffuser, it may be impossible to measure the Transmittance in at leastone propagation direction. Therefore the obscurant may be removed inorder to verify if the diffuser fulfills the conditions of an embodimentby means of a measurement technique proposed in the present description.

A second application concerns the use of the nanodiffuser for modifyingthe spectrum of the transmitted light, i.e. as a sun-color filtercapable of transforming the light of a conventional source, for examplea theater light, making it to assume the color of the light of the suntransmitted through the atmosphere. In this application, the scatteredlight is entirely absorbed, the scattering mechanism remaining, however,possibly being essential for the sun-like colors to appear.

For achieving the effect, it may be mandatory for multiple scattering tonot contribute to the light which is sent to the scene. This goal may beachieved by using, for example, the cylinder configuration described inan embodiment, where the lateral surface of the cylinder may be coveredby an obscurant surface. However, the request of having a length muchlarger than the diameter, L>>Φ, may make the device inconveniently long,for example, for applications related to theater lights, whose diameteris typically few tens of centimeters large. Here are disclosed twosolutions where the contribution of multiple scattering on the lightsent to the scene is removed, while keeping the device very compact. Theresult is achieved either by inserting obscurants inside the diffuser,or by combining separate diffusing and absorbing elements, asillustrated in the following description.

The first solution for the sun-color filter comprises the usage of amulti-channel diffuser, which means an assembly of a plurality ofparallel, individual diffusing elements, each one individuallyfulfilling a condition of an embodiment, which are joined together, forexample, in a honeycomb-like configuration, as shown in FIG. 2, andwhere each individual element is separated from the others by means ofan obscurant surface, whose details are shown at the bottom of FIG. 2.In this configuration, the condition for which the sun-color filterperforms without sending scattered photons in the direction ofillumination coincides with the request that each element operates freefrom multiple scattering in the direction orthogonal to the propagationdirection, which is the condition T(450 nm)≥T_(min), T_(min)=0.4, forexample T_(min)=0.5, such as T_(min)=0.6 of an embodiment. Notably, byusing a sufficiently high filling fraction, this condition may bereached with very thin diffusing elements, and thus very short in thepropagation direction, which allows for very compact multi channelsun-color filters to be developed. Since a characteristic of anembodiment refers to each of the constituting elements of themultichannel sun-color filter, the filter is disassembled if a conditionof embodiment is to be tested by means of the measurement techniqueproposed in present description. Notably, all the tinges of the naturalsunlight which vary in the different hours of the day may be obtainedsimply by adding in series a plurality of multi-channel sun-colorfilters here disclosed.

In the second solution for the sun-color filter, the same effect may beobtained using a combination of a plurality of thin diffusing disks andof 3-dimensional absorbing multi-channel structures. Here eachelementary disk is a diffuser according to an embodiment, and preciselya diffuser operated as a noon skylike diffuser, which means showingT(450 nm)≤T_(Max) in the propagation direction. The absorbing elementscomprise a plurality of thin parallel empty channels, which mayperfectly transmit light in the propagation direction but which may alsoabsorb all components propagating off axis. The device operates using analternate sequence of thin diffusing disks and obscurant grids inbetween. By means of this setting, all photons which are scattered oncein each disk diffuser will hit an absorbing wall in the grid beyond it,thus preventing the possibility of a second scattering event in thefurther diffusing element placed beyond the absorbing grid. In doing so,only the genuine transmitted photons exit the device, the produced lightassuming the pure color as that of the sun. Increasing the number ofdiffusers and grid pairs, all the changes in the tinge of the sun lightin different hours of the day may be reconstructed with high fidelity.It is noted that this arrangement allows to add/remove grids separatelyfrom the diffusers. Therefore it may allow to tune the amount ofscattered photons which are sent to the scene in a similar manner as ithappens in nature when the light from the sun passes through small holesin the clouds at the horizon, which is seen to increase the saturationof the color of sunlight. This option therefore may allow for theaddition of a further degree of freedom useful for increasing thefidelity in the reproduction of sun light.

The layout relative to an embodiment where the nanodiffuser material iscast inside the absorbing multi-channel structure is shown in FIG. 3A,while the layout relative to an embodiment where the absorbing grids areplaced in between standard nano-diffuser disks is depicted in FIG. 3B.

Microscopic structural properties of the diffuser are disclosed herebelow. A set of four relevant structural parameters concerning thenanoparticles dispersed in the solid matrix is defined. Also defined aretheir relevant ranges for which the desired optical properties of adiffuser of an embodiment may be guaranteed. Said parameters are:

(i) m: the ratio between the particle and host medium refractiveindexes,

$m \equiv {\frac{n_{p}}{n_{h}}.}$In the following it is considered as adequate those values falling inthe range 0.5≤m≤2.5, for example 07≤m≤2.1, such as 0.7≤m≤1.9, where therange 0.95≤m≤1.05 is excluded in some or all cases being in this casethe index of the host matrix and of the nanoparticle too close forproviding sufficient scattering.

(ii) D[meters] the effective particle diameter, D=dn_(h), whered[meters] is the average particle size defined as the average particlediameter in the case of spherical particles, and as the average diameterof volume-to-area equivalent spherical particles in the case of nonspherical particles, as defined in [T. C. GRENFELL, AND S. G. WARREN,“Representation of a nonspherical ice particle by a collection ofindependent spheres for scattering and absorption of radiation”. Journalof Geophysical Research 104, D24, 31,697-31,709. (1999), which isincorporated by reference]. The effective particle diameter is given inmeters or, where specified in nm.

(iii) N[meters⁻²]: the number of particles per unit area seen by theimpinging beam propagating in the given direction;

(iv) f: the volume filling fraction occupied by the nanoparticles, where

$f = {\frac{4}{3}{\pi\left( \frac{d}{2} \right)}^{3}\rho}$and ρ[meters⁻³] is the particle number density (number of particles perunit volume).

It is noted that the diffuser length L [meters] does not appearexplicitly but it may be univocally determined by the chosen set ofparameters, being L=Nρ⁻¹ and

$\rho = \frac{f}{\frac{4}{3}{\pi\left( \frac{d}{2} \right)}^{3}}$

The domain in the m,D parameter space for which 5≥γ(m,D)≥γ_(min) isdiscussed in the following.

The Transmittance of a nano-diffuser in a direction for which the lightbeam sees in its path NA particles, where A[meters²] is the beam crosssection, is T(λ)=exp[−Nc_(scat)(λ)], where c_(scat)(λ) is the singleparticle scattering cross section. According to the establishedMie-scattering theory, the single-particle scattering cross sectiondepends only on wavelength, index mismatch, and effective diameter,c_(scat)(λ,m,D). Since γ≡Log [T(450 nm)]/Log [T(630 nm)], it followsthat also γ depends only on index mismatch, and effective diameter,being

${\gamma\left( {m,D} \right)} = {\frac{c_{scat}\left( {{450\mspace{14mu}{nm}},m,D} \right)}{c_{scat}\left( {{630\mspace{14mu}{nm}},m,D} \right)}.}$

In FIG. 4 the γ(m,D) contour is plotted. The curve γ(m,D)=2.5 is drawnin bold. The domain here represented is the 1.05<m≤2.1 and 11 nm≤D≤420nm space. The region where 5≥γ(m,D)≥2.5, which may be adequate forpurposes of an embodiment, is highlighted as grey area on the left ofthe γ(m,D)=2.5 curve. The curve γ(m,D)=3.85, which correspond to theRayleigh limit, is drawn as a dotted line.

The curve γ(m,D)=2.5 is fitted in order to have an analytical expressionfor the m,D pairs in the selected area fulfilling 5≥γ(m,D)≥2.5.Expressing D in nm the fit gives:

For 0.7≤m≤0.95, D≤=−132 m+115; For 1.05≤m<1.35, D≤240; For 1.35≤m≤2.1,D≤=−135 m+507;

In a first test, the quantity T(λ)=exp[−Nc_(scat)(λ)], which gives thespectral profile of the transmitted light for the case of an impinginglight with constant spectral intensity for all wavelengths, has beencomputed for a number of m,D pairs inside and outside the selected area.The resulting spectral distribution has been transformed in RGBamplitudes according to [A. STOCKMAN AND L. T. SHARPE Vision Researchvol. 40, 1711-1737 (2000), which is incorporated by reference] forproviding eye-like visualization of the spectrum. The result confirmsthat while for 5≥γ(m,D)≥2.5 on increasing N, the transmitted lightchanges its color from white, to yellowish, to orange and finally red,in accordance to what is expected for a correct reconstruction of theTransmittance of the atmosphere, for 2.5≤γ(m,D)≤0 the transmitted lightshowed much less saturated tinges, featured by the appearance, forexample, of bluish/pink tonalities.

In a second test the angle-resolved differential cross sectionc_(scat)(θ, λ) was calculated. In the condition wheremultiple-scattering and high filling fraction effects are negligible,this quantity gives the spectral profile of the light scattered by thediffuser for each selected angle, θ. These spectra have been transformedin RGB amplitudes for providing eye-like visualization of the spectrum.The corresponding polar color maps are re-drawn in the form of contourareas to allow black and white data representation.

FIG. 5 shows the calculated, angularly resolved, scattering color maps,for four m,D pairs. The result are presented only for positive angles,0°≤θ≤90°, i.e. for forward scattering, because in the Rayleigh limitforward and backward scattering are identical, while on moving away fromthis limit the scattering tends to become almost only in the forwarddirection.

(i) The first case, which refers to m=1.4, D=50 nm, γ=3.8, representsthe Rayleigh limit, featured by the azure scattering over alldirections, the scattering being slightly less efficient for anglesclose to 90 deg.

(ii) The second case, which refers to m=1.8, D=230 nm, γ=3.5, representsa case for which, in spite of the much larger effective diameter, γ isstill very close to the Rayleigh limit. Apart from the fact that thescattering has become slightly more forward, the result shows a colordistribution barely distinguishable from the previous case.

(iii) The third case, which refers to m=1.7, D=255 nm, γ=3, represents acase for which, in spite of the small change in m,D values with respectto the previous case, γ takes a significantly lower value, whileremaining however within the selected area. The result shows that thecolor distribution is still that characteristic of the noon skydiffusion, but the scattering has become strongly forward, being limitedin the 0°≤θ≤45° cone. Notably, a number of applications where ananodiffuser of an embodiment is used for artificial-lightinginstallations, benefits from the fact that large-angle scattering isquenched, since this may represent a loss for the illumination system.

(iv) The fourth case refers to m=1.9, D=260 mm, γ=2. In spite of thesmall change in m,D values with respect to the previous case, γ hasdropped significantly, being now outside the selected area. The resultshows that the sky-like azure and light-blue tinges totally disappear.The cone 0°≤θ45°, where the scattering is more intense, is now populatedby a whitish-bluish light, where color saturation is very poor. Theoutside 45°≤θ≤90° cone shows greenish and violet-grey tinges, totallyincompatible with the natural color of sky-light.

Surprisingly, accordingly to the reported results from the two set ofnumerical tests, what was found is that, in the chosen m,D range, theextremely simple condition 5≥γ(m,D)≥2.5, which is calculated only on thebasis of two values for the diffuser Transmittance at two selectedwavelengths, may permit an accurate discrimination of the nanodiffuserquality not only for what concerns the diffuser capability ofreproducing a high-fidelity sun-like Transmittance in the entire visiblespectrum, but also for reproducing a high-fidelity sky-like diffusionspectrum, the latter property having been selectively verified for eachdifferent scattering angle.

The conditions on particle number per unit surface, N≤N_(Max) andN≥N_(min), fulfilling T≥T_(min) and T≤T_(max), respectively arediscussed in the following.

By computing diffuser Transmittance, T(λ)=exp[−Nc_(scat)(λ)],accordingly to Mie theory, it is obtained for λ=450 nm and D in [meters]

$N = {{- 4} \times 10^{- 28}\ln\frac{(T)}{D^{6}}{{\frac{m^{2} + 2}{m^{2} - 1}}^{2}\left\lbrack {meters}^{- 2} \right\rbrack}}$

(i) The condition T(450 nm)≥T_(min), T_(min)=0.4, for exampleT_(min)=0.5, such as T_(min)=0.6, translates into

${N \leq N_{Max}} = {{- 4} \times 10^{- 28}\frac{\ln\left( T_{\min} \right)}{D^{6}}{{\frac{m^{2} + 2}{m^{2} - 1}}^{2}\left\lbrack {meters}^{- 2} \right\rbrack}}$

-   -   For example, for T_(min)=0.4, it is obtained

$N_{\max} = {\frac{3.7 \times 10^{- 28}}{D^{6}}{{\frac{m^{2} + 2}{m^{2} - 1}}^{2}\left\lbrack {meters}^{- 2} \right\rbrack}}$

-   -   For example, FIG. 6 shows the volume in the (m,D,N) space        corresponding to the case        5≥γ(m,D)≥3 and 0≤N≤N_(max) for the case of T_(min)=0.6, (and for        1.05≤m≤2.1, 11 nm≤D≤410 nm)

(ii) The condition T(450 nm)≤T_(Max), T_(Max)=0.9, for exampleT_(Max)=0.8, such as T_(Max)=0.7, translates into

${N \geq N_{\min}} = {{- 4} \times 10^{- 28}\frac{\ln\left( T_{Max} \right)}{D^{6}}{{\frac{m^{2} + 2}{m^{2} - 1}}^{2}\left\lbrack {meters}^{- 2} \right\rbrack}}$

-   -   For example, for T_(max)=0.9, it is obtained

$N_{\min} = {\frac{4.24 \times 10^{- 29}}{D^{6}}{{\frac{m^{2} + 2}{m^{2} - 1}}^{2}\left\lbrack {meters}^{- 2} \right\rbrack}}$

-   -   For example, FIG. 7 shows the volume in the (m,D,N) space        corresponding to the case 5≥γ(m,D)≥3 and N_(min)≤N≤10²⁸ m⁻² for        the case of T_(Max)=0.8 (and for 1.05≤m≤2.1, 11 nm≤D≤410 nm)

The condition on maximum volume filling fraction, f is discussed in thefollowing.

The final effect here considered is that related to the presence of highvolume-filling-fraction, f. By increasing f, the distribution ofnanoparticles in the nanodiffuser loses its randomness, and the particlepositions become correlated. As a consequence, the light scattered bythe particle distribution experiences a modulation which depends notonly on the single-particle characteristics, as predicted by the Mietheory, but also on the so called “structure factor” S_(λ)(θ), which isthe Fourier transform of the pair correlation function. The effect ofhigh filling fraction is that of severely depleting the scatteringefficiency. Moreover, especially for smaller particle sizes, it impactsalso the dependence of scattering efficiency on wavelength, and on angleas well. In order to avoid these “close packing” effects, it may berecommended to work with filling fractions f≤10⁻¹, for example f≤10⁻²,such as f≤10⁻³.

A nanodiffuser according to an embodiment is a solid optical elementwhich comprises a transparent solid matrix embedding a dispersion oftransparent nanoparticles, whose average size d is in the range 10nm≤d≤240 nm. The optical element may have any shape, and volume. As listof possible examples, it is mentioned that it may be shaped as aparallelepiped, with any ratio among the length of different axis, thusincluding the case of panels and films, but it may be shaped as wellhaving curved surfaces, i.e. as a cylinder, which may be completelyfilled or empty inside. It may be shaped as a tube, which may bestraight or bent, or as a fiber. It may be also shaped as a lens.Moreover, it may comprise an assembly of different elements, which maycomprise different materials. The dispersion of nanoparticles in theembedding matrix may be homogenous, or it may present, for example,gradients in filling fractions. In the case of gradients or nonhomogeneities, the limits on the highest filling fraction discussed inthe Optical section above are intended to be referred to the highestfilling fraction present in the diffuser. Note that all other quantitiesdefined in the Optical section of above are average quantities, whichtherefore refer to the nanodiffuser as a whole, and are correctlydefined also in the presence of a relevant non homogeneity of theconsidered diffuser.

Particularly, four shaping embodiments are

1. Macroscopic single component: an optical element comprising a uniformorganic/inorganic matrix in which inorganic/organic nanoparticles arehomogenously dispersed.

2. Heterogeneous conglomerate: an optical element comprising a uniformorganic/inorganic matrix in which beads of nanocomposite material areincluded, where beads may have any shape and dimension in the 1-10³ μm,for example 1-10² μm, such as 10-10² μm ranges, and may be made usingthe same or a different matrix material, provided that the difference inrefractive index between the two embedding matrices is sufficientlysmall to prevent beads to create undesired light scattering, reflection,refraction or diffraction. Moreover, the filling fraction featuring thebeads may be sufficiently low to prevent those effect related to highfilling fraction, illustrated in the present description, to take place.

3. Film: an optical element comprising a film of nanocomposite material,which may be supported by a frame or an external support,

4. Bi-component: an optical element comprising a substrate on top ofwhich a film of nanocomposite material is deposited.

Few examples are reported in FIG. 8.

The matrix may be either organic or inorganic.

Organic matrices suited for a purpose of an embodiment are those thatinclude, but are not limited to, the following:

Polymers obtained by polymerization and copolymerization of one, two ormore monomers belonging to the following classes:

Class I Monofunctional Acrylic Monomers such as Acrylic Monomers: MethylAcrylate (MA), Ethyl Acrylate (EA), Butyl Acrylate (BA), n-butylacrylate (nBA), iso-butyl acrylate (iBA), t-butyl acrylate (tBA),2-ethyl hexylacrylate (EHA), Methyl Methacrylate (MMA), ethylmethacrylate (EMA), n-butyl methacrylate (nBMA), isobutyl methacrylate(iBMA), t-butyl methacrylate (tBMA), Lauryl Acrylate (LA), diethyleneglycol bis(allyl carbonate);

Class II Bifunctional Acrylic Monomers such as. Diethylene GlycolDiacrylate (DEGDA) Triethylene Glycol Diacrylate (T3EGDA) TetraethyleneGlycol Diacrylate T4EGDA Polyethylene Glycol Diacrylate (P9EGDA),Ethylene Glycol Diacrylate (EGDA), Butane Diol Diacrylate (BDDA), HexaneDiol Diacrylate (HDDA) Decamethylene Diol Diacrylate (DMDDA), NeoPentylGlycol Diacrylate (NPGDA)

Class III Trifunctional Acrylic Monomers such as: trimethylolpropanetrimethacrylate, trimethylolpropane triacrylate, pentaerythritoltriacrylate.

Class IV Tetrafunctional Acrylic Monomers such as pentaerythritoltetraacrylate

Other thermoplastics such as Polycarbonates (PC), Polystyrene,Polyethylene, Polyethylene terephthalate,

Other specialty thermoplastics as cyclo-olefin copolymers (COC)containing ethylene, cyclopentene, cycloheptene, cyclooctene, norbonene.Statistical copolymers are amorphous if more than 10-15 mol % ofcycloolefins are incorporated in the polymer chain. The glass transitiontemperature may be varied over a wide range by selection of norborneneas cycloolefin and variation of the amount of norbornene incorporatedinto the polymer chain. Cycloolefin copolymers are characterized byexcellent transparency, high glass transition temperatures of up to 200°C., and excellent long-life service temperatures. They are resistant topolar solvents and chemicals and may be melt processed. Due to theirhigh carbon/hydrogen ratio, these polymers have a high refractive index(1.53 for an ethylene/norbornene copolymer at 50 mol % incorporation).

Other specialty thermoplastics obtained by the homopolymerization andcopolymerization of allyl carbonates, like ethylene glycol bis(allylcarbonate) and allyl ethoxyethyl carbonate.

This list may be further expanded by including possible copolymers ofthe above mentioned materials and also crosslinked polymers.

Inorganic matrices suited for the purpose of an embodiment are thosethat include, but are not limited to: soda-lime-silica glass,borosilicate glass, fused silica etc.

Transparency may be fundamental when choosing an appropriate matrix forthe sky-sun diffuser of an embodiment. The transparency of the matrixmay be preferentially very high with respect to both the total amount ofpower lost in transmission and with respect to distortion in thetransmitted spectral profile (the matrix should not preferentiallyabsorb any wavelength, and it may be preferred that the material appearscolorless for the thicknesses used for the nano-diffuser underconsideration). A relevant example is polymethylmethacrylate (PMMA),which shows an absorption in the visible field of <0.05% for 3 mm ofthickness, and polycarbonate (PC), for which an absorption of 2% for 1mm thickness has been measured (these data refer to products on themarket and the light transmittance has been measured with the testmethod DIN5036). Depending on the desired application, the actualrequest on matrix transparency may be more or less strict. In fact,materials having the highest transparency might show limitations inother characteristics, for example related to mechanical properties,fire retarding characteristic, etc. In general, what here may berequired is that, for a given nanodiffuser optical element, theabsorption eventually occurring in the matrix, for a given propagationdirection, is small in comparison to the scattering produced on the samebeam in the same propagation direction because of the presence of thenano-particle dispersion, where by small it is meant that the absorptionof light by the matrix is less than 50%, for example than 20%, such asless than 5% of the scattering produced by the nanoparticle dispersion.The effect of the absorption caused by the matrix does not affect thevalue of nanocomposite Transmittance as defined by the measurementtechnique proposed in the present description since the contribution dueto absorption is present both in the sample and in the referencechannel. The same reasoning applies to the contribution of thereflection of the light at the entrance and exit surfaces of the sample.

The mechanical properties of the organic matrices of the nanodiffuser ofthe invention may fall within the following ranges:

TEST METHODS RANGES UNITS Tensile Strength ASTM D638 ISO 527 1-4 35-80MPa at 23° C. Compressive ASTM D695 ISO 604 100-130 Mpa StrengthFlexural modulus ASTM D790 ISO 178 1500-3500 MPa Flexural Stress ASTMD790 ISO 527  60-130 MPa at break Charpy impact ASTM D6110 ISO 179  1-15KJ/m² (notched) Notched Izod ASTM D256 ISO 180/1A  1-20 KJ/m² impactRockwell ASTM D785 ISO 2039-2 105-130 R Scale, hardness MPa

These ranges of value have been taken from the technical data providedby producers of plastic materials such as Degussa, Rohm, Bayer,Altuglas, etc., and refer to measures taken at a temperature of 23° C.and for thicknesses of few mm.

The nanoparticles have a real refractive index n_(p) sufficientlydifferent from that of the matrix, in order to allow light scattering totake place. Moreover, the nanoparticles should not absorb visible light,at least in an amount which will appreciably reduce the power and/orchange the spectrum (i.e. the color) of the total light exiting thediffuser (i.e. the transmitted+the scattered+the reflected), withrespect to the impinging one. The nanoparticles may be either organicand inorganic, the choice depending on the type of matrix. In the caseof an organic matrix the most suited nanoparticles are inorganicparticles. Organic particles, suited for the application, have an indexof refraction too similar to that of the organic matrix, thus leading toa small difference between the indexes of refraction of the two mediaand to a low scattering efficiency.

Inorganic particles suited for this type of application are those thatinclude but are not limited to ZnO, TiO₂, ZrO₂, SiO₂, Al₂O₃ which haveindex of refraction respectively n_(p)=2.0, 2.6, 2.1, 1.5, 1.7 and anyother oxides which are transparent in the visible region. These sameparticles are also used as fillers for the inorganic matrix.

Organic particles on the other hand may be used with an inorganic matrixand may be made from any of the above-mentioned polymers.

The shape of the nanoparticle may be any, even if spherical particlesare preferred. In fact optimization of the optical properties of thediffuser often requires a careful choice of the particle size. Whenparticles with large aspect ratio are used, the dispersion may behave inmany respects as polydispersed.

A list of possible synthesis methods is described below.

The best-suited materials to make a diffuser of an embodiment are theones made from organic matrices, in particular PMMA and PC. PMMA and PCare both plastics that are very easily produced using different methods.As an example PC may be transformed by extrusion, thermoforming andinjection moulding, while for PMMA all common processes may be usedincluding injection moulding, compression moulding and extrusion,although the highest quality PMMA sheets may be produced by the socalled cell casting process. There are also many other processes thatmay be used for the production of the sky-sun diffuser, the choice ofthe process depending mainly on the type of matrix which is being used.The following is a brief list of processes by means of which our sky-sundiffuser may be prepared:

(i) Radical bulk polymerization of acrylic monomers in the presence ofthe same inorganic oxide nanoparticles, also called industrially “cellcasting method”. This method is the one that was optimized for theproduction of prototypes on a laboratory scale.

(ii) Direct mixing dispersion by extrusion. This technique is expectedto lead to a cheaper material and faster production (in situpolymerisation can take several days); it may be particularlyadvantageous when relatively thin foils (mm) have to be produced, and issuitable for the synthesis of polycarbonate nanocomposites, which maylead to fire-retarding performances superior to PMMA and thus to greaterimpact on the construction industry.

(iii) Emulsion polymerization is the most important method ofpolymerizing vinyl and acrylic monomers industrially. The polymerizationis carried out in water in the presence of water-soluble initiator withmonomer micelles stabilized by surfactants. Products generated byemulsion polymerization find usage as coatings or binders in paints,paper, adhesives, textile, floor care, and leather goods markets.Because of their film-forming properties at room temperature, mostcommercial acrylic ester polymers are copolymers of ethyl acrylate andbutyl acrylate with methyl methacrylate. This process is useful for theproduction of materials having a core-shell morphology comprising a coreconsisting in an oxide and a polymer shell either covalently bonded tothe oxide surface coupling agents by the polymer functions or physicallybonded by entanglement. These beads encapsulating the nanoparticles arethen used in processes (i) or (ii) in order to produce the bulknanocomposite.

(iv) Suspension polymerization. In this type of polymerization, monomersare dispersed as 0.1 to 5 mm droplets in water and are stabilized byprotective colloids or suspending agents. In contrast to emulsionpolymerization, initiation is accomplished by means of a monomer-solubleagent and occurs within the suspended monomer droplet. Water serves thesame dual purpose as in emulsion (heat removal and polymer dispersion).The particle size of the final material is controlled through thecontrol of agitation levels as well as the nature and level of thesuspending agent. Once formed, the 0.1 to 5 mm polymer pellets may beisolated through centrifugation or filtration. Also in this case it maybe possible to obtain core-shell systems.

(v) Thin-film spin coating. Thin films are used as a coating for otheroptical elements, provided that sufficient matching between thermalexpansion coefficients is guaranteed for the application underexamination. This process enables to produce films on a laboratory scaleand with a maximum thickness of 10 μm.

(vi) Radiation-Induced Polymerization. Nanocomposites may be formedthrough the application of high energy radiation to either monomer oroligomer mixture. Ultraviolet curing is the most widely practiced methodof radiation based initiation; this method finds application in theareas of coating, since relatively thin (few mm) objects are easilypolymerised using a photo-initiator (e.g. Benzoin, Benzophenone,2-Benzyl-2-(dimethylamino)-4′-morpholinobutyrophenone etc.) under UVradiation. This technique has seen wide developments in the past fewyears since it is a very advantageous process for industrialapplications. In fact the photopolymerization process is solvent free,the production rates are high and the energy required is much less thanin the case of thermally initiated polymerization processes. Thistechnique has become widely used for the production of films and also ofcoatings on a variety of substrates. In the case of thick systemselectron beam initiated polymerisation is also possible.

Sky-sun diffusers according to an embodiment having an inorganic matrixmay be produced, for example, by means of the sol-gel method. There aretwo different possible approaches:

(i) The production of thin films having thicknesses in the range between5-20 μm is possible by means of the Doctor Blade process. By means ofthis process it may be possible only to produce inorganic/inorganicfilms since at the temperatures involved in the sintering processpolymers burn and degrade.

(ii) Bulk materials may also be processed using the sol gel process. Asan example the material ORMOCER® (http://www.ormocer.de/EN, which isincorporated by reference) is produced using a process that starts bybuilding up an inorganic network through controlled hydrolysis andcondensation of organically modified Si alkoxides. In a subsequent stepthe polymerizable groups, which are fixed to the inorganic network,react with each other in a thermal or UV-initiated process. In thistwo-stage process an inorganic-organic copolymer is synthesized. It mayalso be possible during production to add many fillers to the material,in a variety of forms such as particles. By choosing the most suitableprecursor and the desired nanofiller it may therefore be possible toobtain bulk materials having tailored properties.

First Technique: Cell Casting

Cell Casting polymerization is used, for example, for the production ofPMMA. Two different approaches are followed to produce the sky-sundiffuser, here described as method A and B.

Method A—Direct Polymerization of Monomer

The steps to obtain a well monodisperse suspension of nanoparticles inMMA comprise:

Purification of the Monomer

MMA produced by Sigma Aldrich, which contains 0-100 ppm monomethyl etherhydroquinone as inhibitor (in order to give the product a longer shelflife) is used. The inhibitor is removed, since it may disturb thepolymerization process. In order to do so the monomer is distilled atreduced pressure before use. The distilled monomer then undergoes atleast one cycle of freeze and thaw. If kept covered from light and atlow temperature (i.e. in a fridge) the distilled monomer may last up toone week.

Another method used for purifying big quantities of MMA is by means ofcolumn filtration. A glass column is filled for ⅓ with basic activatedalumina. The monomer (MMA) is then added from the top of the column andthe clean monomer is collected in a glass container after having passedthrough the alumina. In this way the inhibitor (monomethyl etherhydroquinone) is removed.

Surface Modification of Particles

Inorganic particles are surface treated in order to increase thecompatibility between the two phases (organic/inorganic) and to reducethe surface energy, which due to the high ratio between the surface areaof the nanofillers and that of the matrix, plays an important role inthe stability of the system. In the literature various surfacemodification techniques are discussed. Common organic capping agents arethiols with long alkyl chains, which cover the nanoparticle surface andare highly compatible with the monomers. Other possibilities of surfacemodifications are by chemical reaction of the functionalities present onthe surface (i.e silanization with silane molecules), for oxidesnanoparticles they are typically hydroxyls, with proper reactivemolecules, or by covering the particle with surfactant molecules thatcan be physically adsorbed on the surface.

A complementary approach to increase the compatibility between inorganicnanoparticles and organic polymers is to cover the nanoparticle surfacewith a polymer coating. This coating may be made by using difunctionalacrylic monomers such as: 2-Hydroxyethyl Acrylate (HEA), 2-HydroxypropylAcrylate (HPA), Butanediol Monoacrylate (BDMA), Glycidyl Methacrylate(GMA), diglycidyl ether of bisphenol A (DGEBA), DimethylaminoethylMethacrylate, DMAEMA Hydroxyethyl acrylate (HEA), DimethylaminoethylAcrylate (DMAEA). In fact amino, glycidyl or hydroxy groups can stronglyinteract with the surface of the inorganic nanoparticles and thepolymerization of the acrylic groups may create a rigid network aroundthe particle.

Inorganic particles may be bought already having a modified surface.Examples of such particles are: Degussa TEGO® SUN Z800 (ZnO), Degussa VPAdNano® Z805 (ZnO), Degussa AEROXIDE® TiO₂ T805.

Dispersing the Nanoparticles

The nanoparticles are added to the distilled monomer in order to form asuspension with a concentration of nanoparticles of 1% in weight ormore. In order to break up the clusters into the primary particles, thesuspension is subject both to sonication and subsequently tocentrifugation. The highly concentrated suspension is first sonicatedusing a 20 kHz sonicator for 15 min. Big clusters of particles are thusbroken up and a whitish suspension is obtained. Since it may not bepossible to break up all aggregates by means of sonication,centrifugation may be needed in order to remove from the suspensionlarge particles and aggregates having average particle sizes that do notfall within the range of average sizes according to an embodiment.

In fact, a relation exists between the average particle size and thetime necessary for particles having such average size to settle on thebottom of a test tube of a certain height. By means of this relation thecentrifugation time necessary for all particles having an average sizebigger than a certain value to sediment to the bottom of the test tubehas been calculated.

Dynamic light scattering (DLS) tests confirmed that the nanoparticles inthe centrifuged suspension having average size larger than the chosenlimit value are removed, and thus that centrifugation technique isadequate for selecting particle in the ranges according to anembodiment.

Adding the Initiator of Reaction

The initiator activates the polymerization process. In an embodiment thereaction that takes place is called chain growth polymerisation. In thisreaction unsaturated monomer molecules add on to a growing polymer chainone at a time. The process may be divided in three main steps:

-   -   1. The initiator is used in this first step since it is        responsible for starting the polymer chain. The initiator is of        the family of thermal free radical initiators, it may belong to        the family of organic peroxides such as BPO (Benzoyl peroxide)        or to the family of azo compounds like AIBN        (Azobisisobutyronitrile). These compounds, when taken to not        very high temperatures (below 100° C.) may be broken into two        radicals. These radicals then form a stable bond with a carbon        atom in the MMA and the reaction starts. This first step is        called chain initiation.    -   2. Propagation of the reaction, long chains are formed due to        the free radicals which combine with the monomer molecules.    -   3. Termination, polymerization comes to and end due to the        processes of combination or disproportionation.

The radical initiator used in an embodiment is Benzoyl peroxide (BPO,C₁₄H₁₀O₄). This choice is convenient since at 54° C. (this is thetemperature at which our reaction takes place) BPO has a half life of156 h and a decomposition rate of 1.23*10⁻⁶, thus it may be possible toconduct the polymerization reaction of the nanocomposite having a PMMAmatrix at a temperature far away from the boiling temperature of MMA andin reasonable amounts of time (about 1 day).

The suspension is poured into a glass mould and the reaction is carriedout in a reactor, preheated at a temperature of 54° C., under continuousflux of nitrogen.

After polymerization the nanodiffuser is subject to a process of curingthat can last up to 3 days at a temperature of 94° C. in order to removeany residual monomer present inside the nanocomposite and to decomposeany remaining BPO.

The surfaces of the nanodiffuser are treated with appropriate lappingtools and abrasive chemicals in order to remove any superficialimpurities that may compromise the optical properties of the diffuser.

Method B—Two-Step Polymerization

This method enables to control much better the auto acceleration effectand the problem of shrinkage, thus giving a final product having a muchhigher quality. This procedure consists of two steps: apre-polymerization step and a polymerization step. For a detaileddescription of the industrial process refer to Martin Rivera-Toledo etal. “Dynamic Modeling and Experimental Validation of the MMA Cell-CastProcess for Plastic Sheet Production” Ind. Eng. Chem. Res. 2006, 45,8539-8553, which is incorporated by reference. In the prepolymerizationstep experimental conditions are set as modest monomer conversion values(15-20%) are obtained, the so obtained product is a very viscous liquidcalled a syrup. The syrup is obtained adding a small quantity ofinitiator to the monomer and by heating the system to a temperaturebelow 100° C. and above 50° C. which depends on the half-life of theinitiator. The system is kept at this temperature until the desireddegree of conversion is reached. After this step the nanoparticles areadded to the system. A radical initiator is responsible for starting thepolymerization. A quantity of about 0.2% of a second radical initiatoris dissolved in approximately 10% (calculated on the weight of syrupthat is available) of pure distilled monomer. This mixture is added tothe syrup containing nanoparticles and the system is kept stirring forabout 1 hour in order to gain a perfect mixture of the two phases. Thedispersion is poured into a mould and polymerization reaction takesplace in a water bath at a temperature of approximately 60° C.

Second Technique: Extrusion

To produce nanodiffusers according to an embodiment by extrusionpolymerization a two step process has been considered. In a first stepPMMA pellets and small quantities of nanoparticles, are mixed togetherusing a double screw extruder to produce new pellets containing thenanoparticles, the so-called masterbatch. Thus the screw is not onlyused to melt the plastic but also to break the nanoparticles and then tomix them with the melted plastic. The master batch is usually at a veryhigh concentration of nanoparticles, much higher than the 0.01% that isrequired. In a second step, suitable quantities of masterbatch are mixedwith PMMA in order to produce pellets having the desired concentration.These nanocomposite pellets will then be shaped in the desired waythrough the moulding process.

Third Technique: the Hybrid Method by Casting and Extrusion

Another method that may be used for the production of diffusersaccording to an embodiment makes use of both cell casting and extrusiontechniques. First, by means of the cell casting process (either processA or B as described above) a thick sample containing a large number ofparticles is prepared. By large number it is meant that the sampleoperates in large multiple scattering regime, if used as it is. However,the particle concentration (the volume filling fraction) should notexceed the value above which, for the given particle size, the resultingparticle position distribution looses its randomness (see section on theoptical properties). Notably, the sample should not contain asignificant number of particle aggregates, or clusters where the localconcentration is larger than the limit imposed by the set maximumfilling fraction, since this circumstance may deteriorate the finaloptical quality of the composite. This nanocomposite is then broken upinto small pieces and is fed into the extruder together with a suitablequantity of PMMA pellets in order to lead to the development of a finaldiffuser whose total number of particles seen by the testing light beamhas the desired value (for example, it is below the limit for multiplescattering, if this process has to be hindered in respect to theilluminating direction considered). This method leads to a finaldiffuser, which appears homogenous at the macroscopic (mm-m) scale, butwhich is inhomogeneous not only at the nm level, but also at theintermediate, μm-mm scale. It is noted that, as long as the particleposition remains not correlated, the diffuser scattering properties aredetermined by the average particle distribution, being the total numberof particle in the beam path what determines the scattering, no matterif these particles are evenly or unevenly distributed in the diffuser.However, from a practical point of view it may be easier to prepareoptically thick nanodiffusers free from aggregates (or free from largeparticles, too dense clusters etc) by means of carefully controlledcell-casting technique, than by simply dispersing the nanoparticles inthe extruder. The use of beads of nanocomposite material may beimplemented also for industrial cell-casting production of thenanodiffuser, where large volume nano-composite diffusers are developed.

Method: Measurement of the “Monochromatic Normalized CollinearTransmittance, T(λ)”

The experimental measurement procedure described in what follows ismeant to define the “Monochromatic Normalized Collinear Transmittance,T(λ)” of the diffuser at the selected wavelength and propagationdirection. Intuitively, the quantity is the ratio between thetransmittance of the diffuser in the propagation direction, which doesnot account for the contribution of the scattered light, and thetransmittance of a reference sample identical to the diffuser except forthe fact that it does not contain the transparent nanoparticles. Moreprecisely, considering as testing beam a non polarizedquasi-monochromatic and collimated light beam, with central wavelengthλ, spectral bandwidth Δλ<10 nm and angular divergence Δθ<5 mrad, whichtraverses the diffuser in a given propagation direction, and defining as“Monochromatic collinear Transmittance” of a sample at the wavelength λin the selected direction the ratio between (i) the radiant power whichpropagates beyond the sample in the same direction and within the sameΔθ<5 mrad divergence solid angle, and (ii) the radiant power of theimpinging beam, the proposed measurement procedure provides the ratiobetween: (i) the Monochromatic Collinear Transmittance of the diffuserand: (ii) Monochromatic Collinear Transmittance of a reference sampleidentical to the diffuser except for the fact that it does not containthe transparent nanoparticles, said ratio being the quantity heredefined as: “Monochromatic Normalized Collinear Transmittance of thediffuser at the given wavelength an for the given propagationdirection”.

The experimental apparatus, illustrated in FIG. 9 and FIG. 10,comprises:

1. A blue laser source emitting at 450±5 nm

2. A depolarizer and an interferential filter transmitting only a 10 nmwide bandwidth centered at 450 nm

3. A red laser source emitting at 630±5 nm

4. A depolarizer and a 10 nm wide interferential filter transmittingonly a 10 nm wide bandwidth centered at 630 nm

5. A cinematic mirror

6. An achromatic focusing lens

7. A pin-hole placed at the focal point of the lens to spatially filterthe beam

8. An achromatic collimating lens

9. A broadband 50% beam splitter

10. The reference sample

11. A neutral density filter

12. A focusing achromatic lens

13. A pin-hole placed at the focal point of the lens to spatially filterthe beam

14. A detector

15. The diffuser to be characterized

16. A neutral density filter

17. A focusing achromatic lens

18. A pin-hole placed at the focal point to spatially filter the beam

19. A detector

20. The reference sample with reflecting back surface

21. The diffuser to be characterized with reflecting back surface

The radiation delivered by either the 450 nm or the 630 nm lasers, whichmay be independently selected by commuting the position of the cinematicmirror, after having passed through a de-polarizing element and aninterferential filter to remove spectral components which might bepresent out of the 10 nm accepted bandwidth, is sent to a spatialfilter, which acts also as beam expander and collimator, which causesbeam divergence <5 mrad for both the sources. The beam is then split intwo equal arms, which are sent to the samples. In the following it iscalled channel 1 (top in the figure) the one used for the reference, andchannel 2 (bottom) the one used for the nanodiffuser. The transmittedcomponents are focused by achromatic lenses (12, 17) on two pin holes(13, 18), whose size is set to select only the radiation transmitted bythe samples within a 5 mrad divergence angle. The choice of such smallsolid angle ensures that the light scattered by the sample at any angledoes not contribute to the signal which is detected after the pin hole.Neutral density filters (11, 16) are used to optimally match thedetector dynamic range. If it happens that the sample has a highreflectivity coating on one face, so that the light is not transmittedthrough the sample, the technique to be used is shown in FIG. 10. Theapparatus is identical to the previous one, with the only differencethat the beam is transmitted, reflected and then transmitted againthrough the sample before being sent to the spatial filter anddetection.

A problem in ascertaining the contribution to attenuation caused by thescattering is that of isolating it from the other two contributionscaused by the reflection at the entrance and exit air-diffuserinterfaces, and by the possible absorption caused by the matrix or otherspurious components in the sample. This problem is solved by anembodiment of a method here proposed because the diffuser is testedagainst a reference sample which is virtually identical to the diffuserwith the only exception that it does not contain the nanoparticles

Procedure

For each of the two wavelengths, the procedure is repeated identical,changing only the light source. Each measurement procedure is performedin two steps.

Step 1: System Calibration

This step is aimed at removing any possible contribution due to theasymmetry existing between the two channels. To this end twosubstantially identical reference samples are positioned in place 10 and15, where suitable holders exist to ensure maximum reproducibility insample positioning. If P₀ is the power of the used laser, T_(A) istransmittance that the reference sample would have in the presence ofthe sole absorption effect and T_(R) transmittance that the referencesample would have in the presence of the sole reflection, the twodetectors will now measure the two signals:

V₁=c₁P₀T_(R)T_(A) and V₂=c₂P₀T_(R)T_(A), where c₁ and c₂ are twoconstants which do not depend on the sample but on the apparatus, andwhich may be slightly different since they account for all the possibleasymmetries in the layout, as for example those due to the unbalancedpower in the two arms, the slightly different detector sensitivity,pin-hole dimensions etc. The result of the calibration measurementgives: c₁/c₂=V₁/V₂

Step 2: Measurement

In the second step the reference sample in channel 2 is replaced by thenano-diffuser which may be characterized. If now the power the laser isP′₀ which might be the same or different from P₀, it is defined asMonochromatic Normalized Collinear Transmittance of the sample at thegiven wavelength the quantity T≡V′₂/(c₂P′₀T_(R)T_(A)). At this stage,the two detectors will give therefore the signals V′₁=c₁P′₀T_(R)T_(A)and V′₂=c₂P′₀T_(R)T_(A)T. By using c₁/c₂=V₁/V₂, it is finally obtainedT=(V′₂V₁)/(V′₁V₂). By repeating the measurement with both laser sources,T(450 mm) and T(630 mm) are finally obtained.

Note. If the sample is macroscopically inhomogeneous, the procedureimplies to take the minimum measured Transmittance if the goal is todetermine T_(min), and the maximum measured Transmittance if the goal isto determine T_(Max).

EXAMPLES Example 1 Production of a Bulk Diffuser of PMMA/TiO₂

A sky-sun diffuser was produced by means of an in situ bulkpolymerization technique.

In an embodiment Methylmethacrilate (MMA) was used for the matrix andDegussa AEROXIDE TiO₂ T805 for the nanoparticles, which have a nominaldimension of 21 nm (as given by the producer). The particles, asreceived from the producer, are in the form of macro agglomerates withdimensions up to 1 μm. In order to use them the agglomerates wereseparated into the primary particles. A first step to reach this goalconsisted in the sonication of a high concentrated (about 1% in weight)suspension of TiO₂ nanoparticles in MMA. The duration of this processdepends on the power of the employed instrument and on the volume of thedispersion. In the present example the suspension of TiO₂ nanoparticlesin MMA was sonicated for 15 minutes. This process alone was not enoughto separate all the agglomerates and to obtain a distribution ofparticles having a mean size of less than 80 nm. A further step wastaken. In this second step only those particles having the desireddimension (≤80 nm) were selected and those having bigger sizes werediscarded. This was carried out by using a centrifuge that reaches anacceleration of about 3421 g for 14 minutes in order to obtain asuspension containing only TiO₂ nanoparticles with sizes of 69.5 nm. Theaverage particle size was measured using Dynamic Light Scattering (DLS)Technique. The suspension containing the nanoparticles having theselected sizes was diluted in order to obtain 30 ml of suspension with aconcentration ranging from 100 to 400 ppm in weight of TiO₂nanoparticles. In order to reduce the formation of air bubbles withinthe polymer during reaction the suspension was subjected to three cyclesof freeze and thaw. Since thermal cycles cause the aggregation ofparticles, the suspension was sonicated once more (5 min) before thenext step. To start the polymerization reaction benzoyl peroxide (BPO)was used as the initiator in a quantity of 1 mmol/l. Polymerization wascarried out in a reactor under nitrogen atmosphere, using a 150 ml, Ø=54mm Becker as the mould. The reaction lasted 36 hours at the temperatureof 54° C. After polymerization the bulk diffusers were subjected to acuring process at a temperature of 94° C. for 3 days in order toincrease the degree of polymerization and to decompose any residual BPO.The bulk diffuser was then treated in order to remove impurities fromthe surface, which might degrade the optical quality of the diffuser.

The sky-sun nanodiffusers produced using this method had a thickness of1 cm. In the following table the values of γ and T(450 nm) are shown.Concentration was varied in order to show the impact of an increase inthe number of particles on the transmission properties of the sky-sundiffuser. As expected from the results presented in FIG. 5, due tochosen particle size and refraction index mismatch, the scatteringbehaves very close to the Rayleigh limit for all concentrations, thusconfirming that no particle aggregations occurred

PARTICLE EFFECTIVE CONCENTRATION SIZE, D [nm] m (PPM) γ T₄₅₀ 98 1.9  303.87 0.82 98 1.9 100 3.87 0.52 98 1.9 300 3.86 0.14

For what concerns the diffuser visual appearance, FIG. 11 (top) outlinesthe effect of Rayleigh back scattering when three sky-sun nanodiffuserdisks were front illuminated by a commercial InGaN white LED, and seenagainst a dark background. The result shows that the color of theback-scattered light is Azure, similar to that of the noon sky. FIG. 11(bottom) shows a collage (increasing exposure time from right to left)of snapshots obtained when the same disks were illuminated by the sameLED from right side, so that light was guided inside the disks due tototal internal reflection at the disk surface. Rayleigh scattering nowdiffuses out of the disks first the Azure, than the Yellow, and finallythe Orange and the Red colors.

By using the same procedure as above but for the case of TiO₂ particlesbought from Sigma Aldrich, which do not have an hydrophobic coating, andwithout performing the centrifugation process, sky-sun nanodiffuserswere not obtained with correct parameters. In fact, DLS measurements onthe suspension of nanoparticles and MMA before polymerization showedthat the particles in the diffuser had a mean size of 300 nm, which isoutside the range of average particle diameter according to anembodiment. After polymerization, the nanodiffuser appeared whitish forall the investigated concentrations.

Production of a Bulk Diffuser of PMMA/ZnO

In this example the same procedure described above was used, with theexception of TiO₂ being replaced by hydrophobized ZnO nanoparticlesbought from Degussa (TEGO® SUN Z 800). Also, different centrifugationtimes were used. DLS measurements on the suspension of nanoparticles andMMA before polymerization showed that the particles in the diffuser hada mean size of 160 nm. For a volume concentration of 0.0017% and anano-diffuser of thickness 7 mm measurement of the MonochromaticNormalized Collinear Transmittance gave T(450 nm)=0.83 and γ=2.8, whichfalls within the defined acceptable range. The nanodiffuser whenilluminated in a backscattering configuration appeared azure.

Some embodiments have been described, but it is evidently susceptible tonumerous modifications and variants within the scope of the disclosure.

From the foregoing it will be appreciated that, although specificembodiments have been described herein for purposes of illustration,various modifications may be made without deviating from the spirit andscope of the disclosure. Furthermore, where an alternative is disclosedfor a particular embodiment, this alternative may also apply to otherembodiments even if not specifically stated.

The invention claimed is:
 1. A solid optical diffuser which comprises atransparent solid matrix embedding a dispersion of transparentnanoparticles, wherein: said nanoparticles have an average size d in therange 10 nm≤d≤240 nm; the ratio between the blue and red scatteringoptical densities γ≡Log └T (450 nm)┘/Log └T(630 nm)┘ of said solidoptical diffuser falls in the range 5≥γ≥2.5, where T(λ) is themonochromatic normalized collinear transmittance of the solid opticaldiffuser, which is the ratio between the transmittance of the solidoptical diffuser, without the contribution of scattered light, and thetransmittance of a reference sample identical to the solid opticaldiffuser except for the fact that it does not contain nanoparticles;along at least a first propagation direction, the monochromaticnormalized collinear transmittance of the solid optical diffuser isT(450 nm)≥0.4; and along at least a second propagation direction, themonochromatic normalized collinear transmittance of the solid opticaldiffuser is T(450 nm)≤0.9.
 2. The solid optical diffuser according toclaim 1, wherein the relative refraction index${m \equiv \frac{n_{p}}{n_{h}}},$ where n_(p) is the refractive index ofsaid nanoparticles and n_(h) is the refractive index of said transparentsolid matrix, falls in the range 0.7≤m≤2.1, and the effective particlediameter, D≡dn_(h), fulfills D[nm]≤132 m+115 if 0.7≤m<1; D[nm]≤240 if1<m<1.35 and D[nm]≤−135 m+507 if 1.35≤m≤2.1.
 3. The solid opticaldiffuser according to claim 2, wherein, along at least the firstpropagation direction, the number of nanoparticles per unit area is${{N \leq N_{\max}} = {\frac{3.7 \times 10^{- 28}}{D^{6}}{{\frac{m^{2} + 2}{m^{2} - 1}}^{2}\left\lbrack {meters}^{- 2} \right\rbrack}}},$D being given in meters.
 4. The solid optical diffuser according toclaim 3, wherein, along at least the second propagation direction, thenumber of nanoparticles per unit area is${{N \geq N_{\min}} = {\frac{4.24 \times 10^{- 29}}{D^{6}}{{\frac{m^{2} + 2}{m^{2} - 1}}^{2}\left\lbrack {meters}^{- 2} \right\rbrack}}},$D being given in meters.
 5. The solid optical diffuser according toclaim 1, wherein the maximum filling fraction is f≤10⁻².
 6. The solidoptical diffuser according to claim 1, moreover being shaped as aparallelepiped panel where the ratio between the largest dimension, L,and the smallest dimension, W, is L/W≥20.
 7. The solid optical diffuseraccording to claim 1, wherein the ratio between the blue and redscattering optical densities γ is comprised in the range 3.5≤γ≤5, andwherein: along said first propagation direction, the monochromaticnormalized collinear transmittance of the solid optical diffuser isT(450 nm)≥0.6; and along said second propagation direction, themonochromatic normalized collinear transmittance of the solid opticaldiffuser is T(450 nm)≤0.7.
 8. The solid optical diffuser according toclaim 1, wherein said second propagation direction is the same as saidfirst propagation direction.
 9. The solid optical diffuser according toclaim 1, wherein said second propagation direction is orthogonal to saidfirst propagation direction, and wherein along said second propagationdirection the monochromatic normalized collinear transmittance of thesolid optical diffuser is T(λ)≤0.5 for λ≤570 nm.
 10. The solid opticaldiffuser according to claim 9, wherein along said second propagationdirection the monochromatic normalized collinear transmittance of thesolid optical diffuser is T(λ)≤0.1 for λ≤570 nm.
 11. The solid opticaldiffuser according to claim 9, wherein the relative refraction index${m \equiv \frac{n_{p}}{n_{h}}},$ where n_(p) is the refractive index ofsaid nanoparticles and n_(h) is the refractive index of said transparentsolid matrix, falls in the range 0.7≤m≤2.1, and the effective particlediameter, D≡dn_(h), fulfills D[nm]≤132m+115 if 0.7≤m<1; D[nm]≤240 if1<m<1.35 and D[nm]≤−135 m+507 if 1.35≤m≤2.1.
 12. The solid opticaldiffuser according to claim 11, wherein, along at least the firstpropagation direction, the number of nanoparticles per unit area is${{N \leq N_{\max}} = {\frac{3.7 \times 10^{- 28}}{D^{6}}{{\frac{m^{2} + 2}{m^{2} - 1}}^{2}\left\lbrack {meters}^{- 2} \right\rbrack}}},$D being given in meters.
 13. The solid optical diffuser according toclaim 12, wherein, along at least the second propagation direction, thenumber of nanoparticles per unit area is${{N \geq N_{\min}} = {\frac{4.24 \times 10^{- 29}}{d^{6}}{{\frac{m^{2} + 2}{m^{2} - 1}}^{2}\left\lbrack {meters}^{- 2} \right\rbrack}}},$D being given in meters.
 14. The solid optical diffuser according toclaim 9, wherein the maximum filling fraction is f≤10⁻³.
 15. The solidoptical diffuser according to claim 9, moreover being shaped as aparallelepiped panel where the ratio between the largest dimension, L,and the smallest dimension, W, is L/W≥10.
 16. The solid optical diffuseraccording to claim 15, configured to be side-lit by a light source sothat the light generated by the light source is partially guided insidethe parallelepiped panel by total internal reflection and partiallyscattered out of the parallelepiped panel because of the action of thenanoparticles dispersed in the panel.
 17. An illumination systemcomprising a solid optical diffuser according to claim 9 and a lightsource, the solid optical diffuser and the light source being configuredso that the light emitted by the light source is at least partiallyguided inside the solid optical diffuser.
 18. A solid optical diffuserwhich comprises a transparent solid matrix embedding a dispersion oftransparent nanoparticles, wherein: said nanoparticles have an averagesize d in the range 10 nm≤d≤240 nm; the relative refraction index${m \equiv \frac{n_{p}}{n_{h}}},$  where n_(p) is the retractive indexof said nanoparticles and n_(h) is the refractive index of saidtransparent solid matrix, falls in the range 0.7≤m≤2.1, and theeffective particle diameter, D≡dn_(h), fulfills D[nm]≤132 m+115 if0.7≤m<1; D[nm]≤240 if 1<m<1.35; and D[nm]≤−135 m+507 if 1.35≤m≤2.1;along at least a first propagation direction, the number ofnanoparticles per unit area is${N \leq N_{\max}} = {\frac{3.7 \times 10^{- 28}}{D^{6}}{\frac{m^{2} + 2}{m^{2} - 1}}^{2}}$ [meters⁻²], D being given in meters; and along at least a secondpropagation direction, the number of nanoparticles per unit area is${N \geq N_{\min}} = {\frac{4.24 \times 10^{- 29}}{D^{6}}{\frac{m^{2} + 2}{m^{2} - 1}}^{2}}$ [meters⁻²], D being given in meters.
 19. The solid optical diffuseraccording to claim 18, wherein the maximum filling fraction is f≤10⁻².20. The solid optical diffuser according to claim 18, wherein the ratiobetween the blue and red scattering optical densities γ≡Log[T(450nm)]/Log[T(630 nm)] of said solid optical diffuser falls in the range5≥γ≥2.5, where T(λ) is the monochromatic normalized collineartransmittance of the solid optical diffuser, which is the ratio betweenthe transmittance of the solid optical diffuser, without thecontribution of scattered light, and the transmittance of a referencesample identical to the solid optical diffuser except for the fact thatit does not contain nanoparticles.
 21. The solid optical diffuseraccording to claim 18, wherein the solid optical diffuser is shaped as aparallelepiped panel where the ratio between the largest dimension, L,and the smallest dimension, W, is L/W≥20.
 22. The solid optical diffuseraccording to claim 18, further comprising: a mirror surface having thetransparent solid matrix applied thereon.
 23. The solid optical diffuseraccording to claim 22, wherein the solid optical diffuser is shaped as aflat panel, whose length (L), height (H), and width (W) fulfill L≥H>>W.24. The solid optical diffuser according to claim 18, furthercomprising: a reflective coating deposited on one face of thetransparent solid matrix.
 25. The solid optical diffuser according toclaim 24, wherein the reflective coating is a high-reflectivity coating.26. The solid optical diffuser according to claim 24, wherein the solidoptical diffuser is shaped as a flat panel, whose length (L), height(H), and width (W) fulfill L≥H>>W.
 27. The solid optical diffuseraccording to claim 25, wherein the high-reflectivity coating isdeposited on one of the two largest faces of the transparent solidmatrix.
 28. The solid optical diffuser according to claim 18, whereinthe solid optical diffuser is shaped as a flat panel, whose length (L),height (H), and width (W) fulfill L≥H>>W.
 29. The solid optical diffuseraccording to claim 18, further comprising a reflective back surface.